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Solving integrals/ cos(2x+(pi/6))

Integral of cos(2x+(pi/6)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     /      pi\   
 |  cos|2*x + --| dx
 |     \      6 /   
 |                  
/                   
0
$$\int\limits_{0}^{1} \cos{\left(2 x + \frac{\pi}{6} \right)}\, dx$$ 
Integral(cos(2*x + pi/6), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of cosine is sine:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          /      pi\
 |                        sin|2*x + --|
 |    /      pi\             \      6 /
 | cos|2*x + --| dx = C + -------------
 |    \      6 /                2      
 |                                     
/
$$\int \cos{\left(2 x + \frac{\pi}{6} \right)}\, dx = C + \frac{\sin{\left(2 x + \frac{\pi}{6} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         /    pi\
      sin|2 + --|
  1      \    6 /
- - + -----------
  4        2
$$- \frac{1}{4} + \frac{\sin{\left(\frac{\pi}{6} + 2 \right)}}{2}$$ 
=
= 
         /    pi\
      sin|2 + --|
  1      \    6 /
- - + -----------
  4        2
$$- \frac{1}{4} + \frac{\sin{\left(\frac{\pi}{6} + 2 \right)}}{2}$$ 
-1/4 + sin(2 + pi/6)/2
Numerical answer [src] 
0.0397006264766454
0.0397006264766454

    Use the examples entering the upper and lower limits of integration.

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